A modem and/or other signaling device, such as a Digital Subscriber Line Access Multiplexer (DSLAM), may communicate digital information (e.g., binary data bits) via a communications channel, for example, a cable. In real-world applications, noise, which may be present in the communication channel, may interfere with the digital information communicated by the modem. This interference may, for example, cause bit errors in the transmitted digital information.
At least in some applications, bit errors may be tolerated, so long as the bit error rate is kept below a predetermined threshold, for example, no more than 1 bit error for every 10,000,000 bits transmitted (i.e., a bit error rate below 1×10−7).
To test the bit error rate of the modem, for example, noise having a known power spectral density and a known statistical distribution (e.g., Gaussian) may be intentionally injected into the communications channel, after which the bit error rate may be measured in a conventional manner using, for example, a bit error rate measurement device. For this purpose, the noise may be generated or simulated.
The bit error test may require various noise waveforms having different statistical characteristics, such as, for example, an additive white Gaussian (AWGN) noise waveform Xgaus(t). The Fourier Transform Xgaus(f), the Power Spectral Density Sgaus(f), and the autocorrelation function φGaus(τ) of the Gaussian noise waveform XGaus(t) are given by the following equations:
            F      ⁡              (                              X            Gaus                    ⁡                      (            t            )                          )              =                            X          Gaus                ⁡                  (          f          )                    =                        ∫                      -            ∞                                +            ∞                          ⁢                                            X              Gaus                        ⁡                          (              t              )                                ⁢                      ⅇ                                          -                j                            ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢              f              ⁢                                                          ⁢              t                                ⁢                                          ⁢                      ⅆ            t                                                  S        Gaus            ⁡              (        f        )              =                                                                X              Gaus                        ⁡                          (              f              )                                                2            =              F        ⁡                  (                                    φ              Gaus                        ⁡                          (              τ              )                                )                                        φ        Gaus            ⁡              (        τ        )              =                  lim                  T          →          ∞                    ⁢                        ∫                      -            T                                +            T                          ⁢                                            X              Gaus                        ⁡                          (              t              )                                ⁢                                    X              Gaus                        ⁡                          (                              t                +                τ                            )                                ⁢                      ⅆ            t                              
Referring to FIGS. 7a and 7b, it may be seen that the Power Spectral Density Sgaus(f) of the additive white Gaussian noise (AWGN) waveform Xgaus(t) is constant throughout frequency, whereas the autocorrelation function φGaus(τ) of the Gaussian noise waveform XGaus(t) is an impulse function centered at zero (i.e., δ(τ)).
Referring now to FIGS. 8a and 8b, there is seen the Power Spectral Density Sgau-BL(f) and the autocorrelation function φGaus-BL(τ), respectively, for an exemplary low-pass filtered Gaussian noise waveform Xgaus-BL(t) (i.e., band-limited Gaussian noise). As can be seen in FIG. 8a, the Gaussian noise waveform has been filtered to exhibit only those frequencies at or below frequency (F). In this manner, the Power Spectral Density Sgaus-BL(f) of the band-limited Gaussian noise waveform Xgaus-BL(t) is constant between (−F) and (F), whereas the autocorrelation function φGaus-BL(τ) of the band-limited Gaussian noise waveform XGaus-BL(t) is a Sinc function.
The various noise waveforms may be simulated, for example, by generating noise samples of a known statistical distribution (e.g., Gaussian Noise) and power spectral density, and providing these samples to an external device, such as an Arbitrary Waveform Generator (ARB) and/or digital to analog converter (D/A), to produce a desired noise waveform.
However, it is believed that this simulation method may be disadvantageous in that Standard Digital Signal Processors (DSPs), which may be used to generate the noise, may be unable to generate noise samples in real time for wide bandwidth modems that communicate information using very high data link rates.
Alternatively, the noise may be simulated by generating an entire set of noise samples, and then storing the noise samples on a storage medium, for example, a hard disk. In this manner, the noise samples may, for example, be read from the storage medium and then provided to an external device, such as the ARB or D/A, to produce the analog noise waveform.
However, it is believed that this method disadvantageously requires large amounts of storage space for storing the noise samples. For example, 15 MHz band-limited noise, which must be sampled at a rate no less than the Nyquist rate of 30×106 samples per second, requires 30×106 memory locations in the storage medium. If each sample is represented by two Bytes to reduce quantization noise, 60×106 Bytes are required to generate one second of noise. However, since many test applications require upwards of 500 seconds or more of generated noise, 30×107 Bytes (i.e., 30 Gigabytes) of storage space would be required.
Furthermore, at least some test applications may require the generation of multiple noise waveforms, for example, 20 noise waveforms, each having a different statistical distribution and/or power spectral density. Thus, to store 500 seconds of 15 MHz band-limited noise samples for 20 different noise waveforms would require 600×107 Bytes (i.e., 600 Gigabytes) of storage space. Furthermore, for a given noise waveform type, multiple tests, each of which may require an uncorrelated set of noise samples from the noise waveform type, may be required. As a result, the overall storage requirements may become prohibitively expensive.
It is also believed that this simulation method disadvantageously requires that the noise waveform (i.e., the noise samples) be transferred to an active memory, for example, a Random Access Memory (RAM), before being provided to an external device, such as the ARB and/or D/A. However, this would require an additional RAM to store 30 Gigabytes of a single 500 second noise waveform.